Properties

Label 6001.2.a.d.1.1
Level 6001
Weight 2
Character 6001.1
Self dual yes
Analytic conductor 47.918
Analytic rank 0
Dimension 121
CM no
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6001 = 17 \cdot 353 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6001.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(47.9182262530\)
Analytic rank: \(0\)
Dimension: \(121\)
Coefficient ring index: multiple of None
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6001.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.77548 q^{2} -0.417524 q^{3} +5.70327 q^{4} +0.239845 q^{5} +1.15883 q^{6} +2.35024 q^{7} -10.2783 q^{8} -2.82567 q^{9} +O(q^{10})\) \(q-2.77548 q^{2} -0.417524 q^{3} +5.70327 q^{4} +0.239845 q^{5} +1.15883 q^{6} +2.35024 q^{7} -10.2783 q^{8} -2.82567 q^{9} -0.665684 q^{10} +5.59006 q^{11} -2.38125 q^{12} +1.16037 q^{13} -6.52303 q^{14} -0.100141 q^{15} +17.1207 q^{16} +1.00000 q^{17} +7.84259 q^{18} -5.90000 q^{19} +1.36790 q^{20} -0.981281 q^{21} -15.5151 q^{22} +6.51052 q^{23} +4.29146 q^{24} -4.94247 q^{25} -3.22057 q^{26} +2.43236 q^{27} +13.4040 q^{28} -0.502806 q^{29} +0.277939 q^{30} +7.71016 q^{31} -26.9615 q^{32} -2.33399 q^{33} -2.77548 q^{34} +0.563692 q^{35} -16.1156 q^{36} +4.01127 q^{37} +16.3753 q^{38} -0.484481 q^{39} -2.46521 q^{40} +6.35057 q^{41} +2.72352 q^{42} -1.67505 q^{43} +31.8816 q^{44} -0.677724 q^{45} -18.0698 q^{46} -4.93976 q^{47} -7.14833 q^{48} -1.47639 q^{49} +13.7177 q^{50} -0.417524 q^{51} +6.61788 q^{52} +4.29153 q^{53} -6.75096 q^{54} +1.34075 q^{55} -24.1565 q^{56} +2.46340 q^{57} +1.39553 q^{58} +1.89886 q^{59} -0.571132 q^{60} +0.183132 q^{61} -21.3994 q^{62} -6.64100 q^{63} +40.5896 q^{64} +0.278308 q^{65} +6.47792 q^{66} -12.3784 q^{67} +5.70327 q^{68} -2.71830 q^{69} -1.56452 q^{70} +15.2216 q^{71} +29.0432 q^{72} -9.63390 q^{73} -11.1332 q^{74} +2.06360 q^{75} -33.6493 q^{76} +13.1380 q^{77} +1.34466 q^{78} -5.10093 q^{79} +4.10632 q^{80} +7.46145 q^{81} -17.6259 q^{82} -1.18038 q^{83} -5.59651 q^{84} +0.239845 q^{85} +4.64907 q^{86} +0.209934 q^{87} -57.4565 q^{88} +11.5484 q^{89} +1.88101 q^{90} +2.72713 q^{91} +37.1312 q^{92} -3.21918 q^{93} +13.7102 q^{94} -1.41509 q^{95} +11.2571 q^{96} +15.1467 q^{97} +4.09768 q^{98} -15.7957 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + O(q^{10}) \) \( 121q + 9q^{2} + 21q^{3} + 127q^{4} + 27q^{5} + 17q^{6} + 39q^{7} + 24q^{8} + 134q^{9} + 19q^{10} + 48q^{11} + 43q^{12} + 6q^{13} + 40q^{14} + 49q^{15} + 135q^{16} + 121q^{17} + 30q^{19} + 50q^{20} + 18q^{21} + 24q^{22} + 75q^{23} + 24q^{24} + 128q^{25} + 59q^{26} + 75q^{27} + 52q^{28} + 49q^{29} - 34q^{30} + 101q^{31} + 47q^{32} + 20q^{33} + 9q^{34} + 47q^{35} + 138q^{36} + 32q^{37} + 30q^{38} + 101q^{39} + 36q^{40} + 83q^{41} - 11q^{42} + 8q^{43} + 98q^{44} + 49q^{45} + 45q^{46} + 135q^{47} + 54q^{48} + 116q^{49} + 3q^{50} + 21q^{51} - 5q^{52} + 28q^{53} + 10q^{54} + 37q^{55} + 75q^{56} + 31q^{58} + 150q^{59} + 50q^{60} + 36q^{61} + 34q^{62} + 118q^{63} + 110q^{64} + 18q^{65} - 28q^{66} - 6q^{67} + 127q^{68} + 25q^{69} - 22q^{70} + 223q^{71} + q^{72} + 38q^{73} - 10q^{74} + 88q^{75} - 4q^{76} + 38q^{77} + 42q^{78} + 74q^{79} + 106q^{80} + 133q^{81} + 28q^{82} + 55q^{83} + 10q^{84} + 27q^{85} + 64q^{86} + 14q^{87} + 56q^{88} + 118q^{89} + 51q^{90} + 73q^{91} + 82q^{92} + 31q^{93} + 33q^{94} + 106q^{95} + 38q^{96} + 37q^{97} + 88q^{98} + 81q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77548 −1.96256 −0.981279 0.192591i \(-0.938311\pi\)
−0.981279 + 0.192591i \(0.938311\pi\)
\(3\) −0.417524 −0.241058 −0.120529 0.992710i \(-0.538459\pi\)
−0.120529 + 0.992710i \(0.538459\pi\)
\(4\) 5.70327 2.85163
\(5\) 0.239845 0.107262 0.0536310 0.998561i \(-0.482921\pi\)
0.0536310 + 0.998561i \(0.482921\pi\)
\(6\) 1.15883 0.473090
\(7\) 2.35024 0.888306 0.444153 0.895951i \(-0.353505\pi\)
0.444153 + 0.895951i \(0.353505\pi\)
\(8\) −10.2783 −3.63394
\(9\) −2.82567 −0.941891
\(10\) −0.665684 −0.210508
\(11\) 5.59006 1.68547 0.842733 0.538332i \(-0.180945\pi\)
0.842733 + 0.538332i \(0.180945\pi\)
\(12\) −2.38125 −0.687409
\(13\) 1.16037 0.321827 0.160914 0.986968i \(-0.448556\pi\)
0.160914 + 0.986968i \(0.448556\pi\)
\(14\) −6.52303 −1.74335
\(15\) −0.100141 −0.0258563
\(16\) 17.1207 4.28019
\(17\) 1.00000 0.242536
\(18\) 7.84259 1.84852
\(19\) −5.90000 −1.35355 −0.676777 0.736188i \(-0.736624\pi\)
−0.676777 + 0.736188i \(0.736624\pi\)
\(20\) 1.36790 0.305872
\(21\) −0.981281 −0.214133
\(22\) −15.5151 −3.30783
\(23\) 6.51052 1.35754 0.678768 0.734352i \(-0.262514\pi\)
0.678768 + 0.734352i \(0.262514\pi\)
\(24\) 4.29146 0.875990
\(25\) −4.94247 −0.988495
\(26\) −3.22057 −0.631605
\(27\) 2.43236 0.468108
\(28\) 13.4040 2.53312
\(29\) −0.502806 −0.0933688 −0.0466844 0.998910i \(-0.514866\pi\)
−0.0466844 + 0.998910i \(0.514866\pi\)
\(30\) 0.277939 0.0507445
\(31\) 7.71016 1.38479 0.692393 0.721520i \(-0.256556\pi\)
0.692393 + 0.721520i \(0.256556\pi\)
\(32\) −26.9615 −4.76617
\(33\) −2.33399 −0.406295
\(34\) −2.77548 −0.475990
\(35\) 0.563692 0.0952814
\(36\) −16.1156 −2.68593
\(37\) 4.01127 0.659449 0.329724 0.944077i \(-0.393044\pi\)
0.329724 + 0.944077i \(0.393044\pi\)
\(38\) 16.3753 2.65643
\(39\) −0.484481 −0.0775790
\(40\) −2.46521 −0.389784
\(41\) 6.35057 0.991793 0.495896 0.868382i \(-0.334840\pi\)
0.495896 + 0.868382i \(0.334840\pi\)
\(42\) 2.72352 0.420249
\(43\) −1.67505 −0.255443 −0.127722 0.991810i \(-0.540766\pi\)
−0.127722 + 0.991810i \(0.540766\pi\)
\(44\) 31.8816 4.80633
\(45\) −0.677724 −0.101029
\(46\) −18.0698 −2.66425
\(47\) −4.93976 −0.720538 −0.360269 0.932849i \(-0.617315\pi\)
−0.360269 + 0.932849i \(0.617315\pi\)
\(48\) −7.14833 −1.03177
\(49\) −1.47639 −0.210913
\(50\) 13.7177 1.93998
\(51\) −0.417524 −0.0584651
\(52\) 6.61788 0.917734
\(53\) 4.29153 0.589487 0.294744 0.955576i \(-0.404766\pi\)
0.294744 + 0.955576i \(0.404766\pi\)
\(54\) −6.75096 −0.918689
\(55\) 1.34075 0.180786
\(56\) −24.1565 −3.22805
\(57\) 2.46340 0.326285
\(58\) 1.39553 0.183242
\(59\) 1.89886 0.247210 0.123605 0.992331i \(-0.460554\pi\)
0.123605 + 0.992331i \(0.460554\pi\)
\(60\) −0.571132 −0.0737328
\(61\) 0.183132 0.0234476 0.0117238 0.999931i \(-0.496268\pi\)
0.0117238 + 0.999931i \(0.496268\pi\)
\(62\) −21.3994 −2.71772
\(63\) −6.64100 −0.836687
\(64\) 40.5896 5.07371
\(65\) 0.278308 0.0345198
\(66\) 6.47792 0.797377
\(67\) −12.3784 −1.51227 −0.756134 0.654417i \(-0.772914\pi\)
−0.756134 + 0.654417i \(0.772914\pi\)
\(68\) 5.70327 0.691623
\(69\) −2.71830 −0.327245
\(70\) −1.56452 −0.186995
\(71\) 15.2216 1.80648 0.903238 0.429139i \(-0.141183\pi\)
0.903238 + 0.429139i \(0.141183\pi\)
\(72\) 29.0432 3.42278
\(73\) −9.63390 −1.12756 −0.563781 0.825924i \(-0.690654\pi\)
−0.563781 + 0.825924i \(0.690654\pi\)
\(74\) −11.1332 −1.29421
\(75\) 2.06360 0.238284
\(76\) −33.6493 −3.85984
\(77\) 13.1380 1.49721
\(78\) 1.34466 0.152253
\(79\) −5.10093 −0.573900 −0.286950 0.957946i \(-0.592641\pi\)
−0.286950 + 0.957946i \(0.592641\pi\)
\(80\) 4.10632 0.459101
\(81\) 7.46145 0.829050
\(82\) −17.6259 −1.94645
\(83\) −1.18038 −0.129563 −0.0647815 0.997899i \(-0.520635\pi\)
−0.0647815 + 0.997899i \(0.520635\pi\)
\(84\) −5.59651 −0.610629
\(85\) 0.239845 0.0260148
\(86\) 4.64907 0.501322
\(87\) 0.209934 0.0225073
\(88\) −57.4565 −6.12488
\(89\) 11.5484 1.22413 0.612063 0.790809i \(-0.290340\pi\)
0.612063 + 0.790809i \(0.290340\pi\)
\(90\) 1.88101 0.198275
\(91\) 2.72713 0.285881
\(92\) 37.1312 3.87120
\(93\) −3.21918 −0.333814
\(94\) 13.7102 1.41410
\(95\) −1.41509 −0.145185
\(96\) 11.2571 1.14892
\(97\) 15.1467 1.53791 0.768956 0.639301i \(-0.220776\pi\)
0.768956 + 0.639301i \(0.220776\pi\)
\(98\) 4.09768 0.413929
\(99\) −15.7957 −1.58753
\(100\) −28.1883 −2.81883
\(101\) 8.33018 0.828884 0.414442 0.910076i \(-0.363977\pi\)
0.414442 + 0.910076i \(0.363977\pi\)
\(102\) 1.15883 0.114741
\(103\) 7.42252 0.731363 0.365682 0.930740i \(-0.380836\pi\)
0.365682 + 0.930740i \(0.380836\pi\)
\(104\) −11.9266 −1.16950
\(105\) −0.235355 −0.0229683
\(106\) −11.9110 −1.15690
\(107\) −0.957372 −0.0925526 −0.0462763 0.998929i \(-0.514735\pi\)
−0.0462763 + 0.998929i \(0.514735\pi\)
\(108\) 13.8724 1.33487
\(109\) −16.6683 −1.59653 −0.798267 0.602304i \(-0.794249\pi\)
−0.798267 + 0.602304i \(0.794249\pi\)
\(110\) −3.72121 −0.354804
\(111\) −1.67480 −0.158965
\(112\) 40.2378 3.80211
\(113\) −9.04641 −0.851015 −0.425507 0.904955i \(-0.639904\pi\)
−0.425507 + 0.904955i \(0.639904\pi\)
\(114\) −6.83710 −0.640353
\(115\) 1.56152 0.145612
\(116\) −2.86764 −0.266254
\(117\) −3.27881 −0.303126
\(118\) −5.27024 −0.485165
\(119\) 2.35024 0.215446
\(120\) 1.02928 0.0939604
\(121\) 20.2488 1.84080
\(122\) −0.508278 −0.0460174
\(123\) −2.65152 −0.239079
\(124\) 43.9731 3.94890
\(125\) −2.38465 −0.213290
\(126\) 18.4319 1.64205
\(127\) −8.74568 −0.776054 −0.388027 0.921648i \(-0.626843\pi\)
−0.388027 + 0.921648i \(0.626843\pi\)
\(128\) −58.7325 −5.19127
\(129\) 0.699375 0.0615765
\(130\) −0.772437 −0.0677472
\(131\) 4.70655 0.411213 0.205607 0.978635i \(-0.434083\pi\)
0.205607 + 0.978635i \(0.434083\pi\)
\(132\) −13.3113 −1.15860
\(133\) −13.8664 −1.20237
\(134\) 34.3561 2.96791
\(135\) 0.583390 0.0502102
\(136\) −10.2783 −0.881360
\(137\) −1.03190 −0.0881610 −0.0440805 0.999028i \(-0.514036\pi\)
−0.0440805 + 0.999028i \(0.514036\pi\)
\(138\) 7.54458 0.642237
\(139\) 5.12493 0.434691 0.217346 0.976095i \(-0.430260\pi\)
0.217346 + 0.976095i \(0.430260\pi\)
\(140\) 3.21489 0.271708
\(141\) 2.06247 0.173691
\(142\) −42.2473 −3.54532
\(143\) 6.48651 0.542429
\(144\) −48.3776 −4.03147
\(145\) −0.120596 −0.0100149
\(146\) 26.7387 2.21291
\(147\) 0.616429 0.0508422
\(148\) 22.8774 1.88051
\(149\) 6.35458 0.520587 0.260294 0.965530i \(-0.416181\pi\)
0.260294 + 0.965530i \(0.416181\pi\)
\(150\) −5.72748 −0.467647
\(151\) −14.8664 −1.20981 −0.604905 0.796298i \(-0.706789\pi\)
−0.604905 + 0.796298i \(0.706789\pi\)
\(152\) 60.6422 4.91873
\(153\) −2.82567 −0.228442
\(154\) −36.4641 −2.93836
\(155\) 1.84924 0.148535
\(156\) −2.76312 −0.221227
\(157\) 19.7081 1.57288 0.786440 0.617667i \(-0.211922\pi\)
0.786440 + 0.617667i \(0.211922\pi\)
\(158\) 14.1575 1.12631
\(159\) −1.79182 −0.142101
\(160\) −6.46659 −0.511229
\(161\) 15.3013 1.20591
\(162\) −20.7091 −1.62706
\(163\) 17.8742 1.40001 0.700006 0.714137i \(-0.253181\pi\)
0.700006 + 0.714137i \(0.253181\pi\)
\(164\) 36.2190 2.82823
\(165\) −0.559795 −0.0435800
\(166\) 3.27610 0.254275
\(167\) 7.76350 0.600757 0.300379 0.953820i \(-0.402887\pi\)
0.300379 + 0.953820i \(0.402887\pi\)
\(168\) 10.0859 0.778147
\(169\) −11.6536 −0.896427
\(170\) −0.665684 −0.0510556
\(171\) 16.6715 1.27490
\(172\) −9.55327 −0.728430
\(173\) −4.35396 −0.331026 −0.165513 0.986208i \(-0.552928\pi\)
−0.165513 + 0.986208i \(0.552928\pi\)
\(174\) −0.582666 −0.0441718
\(175\) −11.6160 −0.878086
\(176\) 95.7060 7.21411
\(177\) −0.792820 −0.0595920
\(178\) −32.0523 −2.40242
\(179\) 9.29452 0.694705 0.347352 0.937735i \(-0.387081\pi\)
0.347352 + 0.937735i \(0.387081\pi\)
\(180\) −3.86524 −0.288098
\(181\) 24.2494 1.80245 0.901223 0.433356i \(-0.142671\pi\)
0.901223 + 0.433356i \(0.142671\pi\)
\(182\) −7.56909 −0.561058
\(183\) −0.0764620 −0.00565224
\(184\) −66.9173 −4.93321
\(185\) 0.962083 0.0707338
\(186\) 8.93476 0.655129
\(187\) 5.59006 0.408786
\(188\) −28.1728 −2.05471
\(189\) 5.71662 0.415823
\(190\) 3.92754 0.284934
\(191\) 9.19880 0.665602 0.332801 0.942997i \(-0.392006\pi\)
0.332801 + 0.942997i \(0.392006\pi\)
\(192\) −16.9472 −1.22306
\(193\) 8.53210 0.614154 0.307077 0.951685i \(-0.400649\pi\)
0.307077 + 0.951685i \(0.400649\pi\)
\(194\) −42.0393 −3.01824
\(195\) −0.116200 −0.00832128
\(196\) −8.42025 −0.601446
\(197\) 0.380134 0.0270835 0.0135417 0.999908i \(-0.495689\pi\)
0.0135417 + 0.999908i \(0.495689\pi\)
\(198\) 43.8405 3.11561
\(199\) −1.38504 −0.0981827 −0.0490913 0.998794i \(-0.515633\pi\)
−0.0490913 + 0.998794i \(0.515633\pi\)
\(200\) 50.8004 3.59213
\(201\) 5.16830 0.364544
\(202\) −23.1202 −1.62673
\(203\) −1.18171 −0.0829400
\(204\) −2.38125 −0.166721
\(205\) 1.52315 0.106382
\(206\) −20.6010 −1.43534
\(207\) −18.3966 −1.27865
\(208\) 19.8663 1.37748
\(209\) −32.9814 −2.28137
\(210\) 0.653223 0.0450767
\(211\) 14.0694 0.968578 0.484289 0.874908i \(-0.339078\pi\)
0.484289 + 0.874908i \(0.339078\pi\)
\(212\) 24.4758 1.68100
\(213\) −6.35541 −0.435465
\(214\) 2.65716 0.181640
\(215\) −0.401753 −0.0273993
\(216\) −25.0006 −1.70108
\(217\) 18.1207 1.23011
\(218\) 46.2625 3.13329
\(219\) 4.02239 0.271808
\(220\) 7.64664 0.515537
\(221\) 1.16037 0.0780546
\(222\) 4.64838 0.311979
\(223\) 4.20622 0.281669 0.140835 0.990033i \(-0.455021\pi\)
0.140835 + 0.990033i \(0.455021\pi\)
\(224\) −63.3660 −4.23382
\(225\) 13.9658 0.931055
\(226\) 25.1081 1.67017
\(227\) 1.99235 0.132237 0.0661184 0.997812i \(-0.478938\pi\)
0.0661184 + 0.997812i \(0.478938\pi\)
\(228\) 14.0494 0.930445
\(229\) −26.1501 −1.72805 −0.864025 0.503449i \(-0.832064\pi\)
−0.864025 + 0.503449i \(0.832064\pi\)
\(230\) −4.33395 −0.285772
\(231\) −5.48542 −0.360914
\(232\) 5.16801 0.339297
\(233\) 13.6353 0.893279 0.446640 0.894714i \(-0.352621\pi\)
0.446640 + 0.894714i \(0.352621\pi\)
\(234\) 9.10027 0.594903
\(235\) −1.18478 −0.0772863
\(236\) 10.8297 0.704954
\(237\) 2.12976 0.138343
\(238\) −6.52303 −0.422825
\(239\) −18.4831 −1.19557 −0.597785 0.801656i \(-0.703952\pi\)
−0.597785 + 0.801656i \(0.703952\pi\)
\(240\) −1.71449 −0.110670
\(241\) 4.28271 0.275874 0.137937 0.990441i \(-0.455953\pi\)
0.137937 + 0.990441i \(0.455953\pi\)
\(242\) −56.1999 −3.61267
\(243\) −10.4124 −0.667957
\(244\) 1.04445 0.0668641
\(245\) −0.354105 −0.0226229
\(246\) 7.35923 0.469207
\(247\) −6.84616 −0.435611
\(248\) −79.2477 −5.03223
\(249\) 0.492835 0.0312322
\(250\) 6.61855 0.418594
\(251\) −30.4674 −1.92309 −0.961543 0.274654i \(-0.911437\pi\)
−0.961543 + 0.274654i \(0.911437\pi\)
\(252\) −37.8754 −2.38593
\(253\) 36.3942 2.28808
\(254\) 24.2734 1.52305
\(255\) −0.100141 −0.00627108
\(256\) 81.8314 5.11446
\(257\) −9.26754 −0.578093 −0.289047 0.957315i \(-0.593338\pi\)
−0.289047 + 0.957315i \(0.593338\pi\)
\(258\) −1.94110 −0.120848
\(259\) 9.42744 0.585792
\(260\) 1.58726 0.0984380
\(261\) 1.42077 0.0879432
\(262\) −13.0629 −0.807030
\(263\) 7.38379 0.455304 0.227652 0.973743i \(-0.426895\pi\)
0.227652 + 0.973743i \(0.426895\pi\)
\(264\) 23.9895 1.47645
\(265\) 1.02930 0.0632296
\(266\) 38.4859 2.35972
\(267\) −4.82173 −0.295085
\(268\) −70.5976 −4.31243
\(269\) −13.6180 −0.830306 −0.415153 0.909752i \(-0.636272\pi\)
−0.415153 + 0.909752i \(0.636272\pi\)
\(270\) −1.61918 −0.0985404
\(271\) 6.71299 0.407785 0.203893 0.978993i \(-0.434641\pi\)
0.203893 + 0.978993i \(0.434641\pi\)
\(272\) 17.1207 1.03810
\(273\) −1.13864 −0.0689139
\(274\) 2.86401 0.173021
\(275\) −27.6287 −1.66607
\(276\) −15.5032 −0.933183
\(277\) −4.73918 −0.284749 −0.142375 0.989813i \(-0.545474\pi\)
−0.142375 + 0.989813i \(0.545474\pi\)
\(278\) −14.2241 −0.853106
\(279\) −21.7864 −1.30432
\(280\) −5.79382 −0.346247
\(281\) 31.6506 1.88811 0.944057 0.329782i \(-0.106975\pi\)
0.944057 + 0.329782i \(0.106975\pi\)
\(282\) −5.72433 −0.340879
\(283\) −33.4717 −1.98969 −0.994844 0.101418i \(-0.967662\pi\)
−0.994844 + 0.101418i \(0.967662\pi\)
\(284\) 86.8131 5.15141
\(285\) 0.590833 0.0349979
\(286\) −18.0032 −1.06455
\(287\) 14.9253 0.881015
\(288\) 76.1845 4.48922
\(289\) 1.00000 0.0588235
\(290\) 0.334710 0.0196549
\(291\) −6.32411 −0.370726
\(292\) −54.9447 −3.21540
\(293\) −8.12392 −0.474604 −0.237302 0.971436i \(-0.576263\pi\)
−0.237302 + 0.971436i \(0.576263\pi\)
\(294\) −1.71088 −0.0997807
\(295\) 0.455432 0.0265163
\(296\) −41.2292 −2.39640
\(297\) 13.5970 0.788980
\(298\) −17.6370 −1.02168
\(299\) 7.55458 0.436893
\(300\) 11.7693 0.679500
\(301\) −3.93677 −0.226912
\(302\) 41.2613 2.37432
\(303\) −3.47805 −0.199809
\(304\) −101.012 −5.79346
\(305\) 0.0439233 0.00251504
\(306\) 7.84259 0.448331
\(307\) −29.0418 −1.65750 −0.828752 0.559615i \(-0.810949\pi\)
−0.828752 + 0.559615i \(0.810949\pi\)
\(308\) 74.9293 4.26949
\(309\) −3.09908 −0.176301
\(310\) −5.13253 −0.291508
\(311\) −19.9040 −1.12865 −0.564326 0.825552i \(-0.690864\pi\)
−0.564326 + 0.825552i \(0.690864\pi\)
\(312\) 4.97966 0.281918
\(313\) −11.5980 −0.655557 −0.327779 0.944755i \(-0.606300\pi\)
−0.327779 + 0.944755i \(0.606300\pi\)
\(314\) −54.6994 −3.08687
\(315\) −1.59281 −0.0897447
\(316\) −29.0920 −1.63655
\(317\) −25.3477 −1.42367 −0.711835 0.702347i \(-0.752136\pi\)
−0.711835 + 0.702347i \(0.752136\pi\)
\(318\) 4.97315 0.278881
\(319\) −2.81072 −0.157370
\(320\) 9.73522 0.544216
\(321\) 0.399726 0.0223105
\(322\) −42.4683 −2.36666
\(323\) −5.90000 −0.328285
\(324\) 42.5547 2.36415
\(325\) −5.73508 −0.318125
\(326\) −49.6093 −2.74761
\(327\) 6.95942 0.384857
\(328\) −65.2733 −3.60412
\(329\) −11.6096 −0.640058
\(330\) 1.55370 0.0855282
\(331\) −15.2938 −0.840623 −0.420311 0.907380i \(-0.638079\pi\)
−0.420311 + 0.907380i \(0.638079\pi\)
\(332\) −6.73200 −0.369466
\(333\) −11.3345 −0.621129
\(334\) −21.5474 −1.17902
\(335\) −2.96891 −0.162209
\(336\) −16.8003 −0.916529
\(337\) 31.8640 1.73574 0.867872 0.496788i \(-0.165487\pi\)
0.867872 + 0.496788i \(0.165487\pi\)
\(338\) 32.3442 1.75929
\(339\) 3.77710 0.205144
\(340\) 1.36790 0.0741848
\(341\) 43.1003 2.33401
\(342\) −46.2713 −2.50207
\(343\) −19.9215 −1.07566
\(344\) 17.2167 0.928265
\(345\) −0.651971 −0.0351009
\(346\) 12.0843 0.649657
\(347\) −12.9847 −0.697056 −0.348528 0.937298i \(-0.613318\pi\)
−0.348528 + 0.937298i \(0.613318\pi\)
\(348\) 1.19731 0.0641825
\(349\) 8.02647 0.429647 0.214824 0.976653i \(-0.431082\pi\)
0.214824 + 0.976653i \(0.431082\pi\)
\(350\) 32.2399 1.72329
\(351\) 2.82243 0.150650
\(352\) −150.717 −8.03322
\(353\) −1.00000 −0.0532246
\(354\) 2.20045 0.116953
\(355\) 3.65083 0.193766
\(356\) 65.8636 3.49076
\(357\) −0.981281 −0.0519349
\(358\) −25.7967 −1.36340
\(359\) 3.45667 0.182436 0.0912181 0.995831i \(-0.470924\pi\)
0.0912181 + 0.995831i \(0.470924\pi\)
\(360\) 6.96587 0.367134
\(361\) 15.8101 0.832108
\(362\) −67.3037 −3.53740
\(363\) −8.45435 −0.443738
\(364\) 15.5536 0.815229
\(365\) −2.31064 −0.120945
\(366\) 0.212219 0.0110928
\(367\) −32.7225 −1.70810 −0.854052 0.520188i \(-0.825862\pi\)
−0.854052 + 0.520188i \(0.825862\pi\)
\(368\) 111.465 5.81051
\(369\) −17.9446 −0.934161
\(370\) −2.67024 −0.138819
\(371\) 10.0861 0.523645
\(372\) −18.3599 −0.951914
\(373\) 1.99013 0.103045 0.0515226 0.998672i \(-0.483593\pi\)
0.0515226 + 0.998672i \(0.483593\pi\)
\(374\) −15.5151 −0.802265
\(375\) 0.995651 0.0514152
\(376\) 50.7725 2.61839
\(377\) −0.583439 −0.0300486
\(378\) −15.8663 −0.816077
\(379\) 25.5095 1.31034 0.655168 0.755483i \(-0.272598\pi\)
0.655168 + 0.755483i \(0.272598\pi\)
\(380\) −8.07062 −0.414014
\(381\) 3.65153 0.187074
\(382\) −25.5310 −1.30628
\(383\) 19.5482 0.998864 0.499432 0.866353i \(-0.333542\pi\)
0.499432 + 0.866353i \(0.333542\pi\)
\(384\) 24.5223 1.25140
\(385\) 3.15107 0.160594
\(386\) −23.6806 −1.20531
\(387\) 4.73315 0.240600
\(388\) 86.3856 4.38557
\(389\) 36.6173 1.85657 0.928285 0.371871i \(-0.121284\pi\)
0.928285 + 0.371871i \(0.121284\pi\)
\(390\) 0.322511 0.0163310
\(391\) 6.51052 0.329251
\(392\) 15.1748 0.766445
\(393\) −1.96510 −0.0991262
\(394\) −1.05505 −0.0531529
\(395\) −1.22343 −0.0615576
\(396\) −90.0870 −4.52704
\(397\) −21.7361 −1.09090 −0.545452 0.838142i \(-0.683642\pi\)
−0.545452 + 0.838142i \(0.683642\pi\)
\(398\) 3.84414 0.192689
\(399\) 5.78956 0.289841
\(400\) −84.6188 −4.23094
\(401\) 11.7473 0.586633 0.293317 0.956015i \(-0.405241\pi\)
0.293317 + 0.956015i \(0.405241\pi\)
\(402\) −14.3445 −0.715439
\(403\) 8.94661 0.445662
\(404\) 47.5093 2.36368
\(405\) 1.78959 0.0889255
\(406\) 3.27982 0.162775
\(407\) 22.4232 1.11148
\(408\) 4.29146 0.212459
\(409\) −28.6002 −1.41419 −0.707095 0.707119i \(-0.749995\pi\)
−0.707095 + 0.707119i \(0.749995\pi\)
\(410\) −4.22748 −0.208780
\(411\) 0.430843 0.0212519
\(412\) 42.3327 2.08558
\(413\) 4.46277 0.219599
\(414\) 51.0593 2.50943
\(415\) −0.283107 −0.0138972
\(416\) −31.2852 −1.53389
\(417\) −2.13978 −0.104786
\(418\) 91.5390 4.47732
\(419\) 10.9524 0.535060 0.267530 0.963550i \(-0.413793\pi\)
0.267530 + 0.963550i \(0.413793\pi\)
\(420\) −1.34229 −0.0654973
\(421\) 19.6046 0.955470 0.477735 0.878504i \(-0.341458\pi\)
0.477735 + 0.878504i \(0.341458\pi\)
\(422\) −39.0493 −1.90089
\(423\) 13.9581 0.678668
\(424\) −44.1098 −2.14216
\(425\) −4.94247 −0.239745
\(426\) 17.6393 0.854626
\(427\) 0.430403 0.0208287
\(428\) −5.46015 −0.263926
\(429\) −2.70828 −0.130757
\(430\) 1.11506 0.0537728
\(431\) −12.7253 −0.612956 −0.306478 0.951878i \(-0.599151\pi\)
−0.306478 + 0.951878i \(0.599151\pi\)
\(432\) 41.6438 2.00359
\(433\) 29.8667 1.43530 0.717650 0.696404i \(-0.245218\pi\)
0.717650 + 0.696404i \(0.245218\pi\)
\(434\) −50.2936 −2.41417
\(435\) 0.0503516 0.00241417
\(436\) −95.0638 −4.55273
\(437\) −38.4121 −1.83750
\(438\) −11.1640 −0.533439
\(439\) 33.7453 1.61058 0.805288 0.592884i \(-0.202011\pi\)
0.805288 + 0.592884i \(0.202011\pi\)
\(440\) −13.7807 −0.656967
\(441\) 4.17179 0.198657
\(442\) −3.22057 −0.153187
\(443\) −14.9084 −0.708319 −0.354159 0.935185i \(-0.615233\pi\)
−0.354159 + 0.935185i \(0.615233\pi\)
\(444\) −9.55185 −0.453311
\(445\) 2.76982 0.131302
\(446\) −11.6743 −0.552793
\(447\) −2.65319 −0.125492
\(448\) 95.3953 4.50700
\(449\) 13.0950 0.617994 0.308997 0.951063i \(-0.400007\pi\)
0.308997 + 0.951063i \(0.400007\pi\)
\(450\) −38.7618 −1.82725
\(451\) 35.5001 1.67163
\(452\) −51.5941 −2.42678
\(453\) 6.20708 0.291634
\(454\) −5.52971 −0.259522
\(455\) 0.654089 0.0306642
\(456\) −25.3196 −1.18570
\(457\) 32.6396 1.52682 0.763408 0.645917i \(-0.223525\pi\)
0.763408 + 0.645917i \(0.223525\pi\)
\(458\) 72.5791 3.39140
\(459\) 2.43236 0.113533
\(460\) 8.90574 0.415232
\(461\) 17.1339 0.798004 0.399002 0.916950i \(-0.369357\pi\)
0.399002 + 0.916950i \(0.369357\pi\)
\(462\) 15.2246 0.708315
\(463\) −5.86312 −0.272482 −0.136241 0.990676i \(-0.543502\pi\)
−0.136241 + 0.990676i \(0.543502\pi\)
\(464\) −8.60841 −0.399636
\(465\) −0.772105 −0.0358055
\(466\) −37.8445 −1.75311
\(467\) −19.9019 −0.920949 −0.460474 0.887673i \(-0.652321\pi\)
−0.460474 + 0.887673i \(0.652321\pi\)
\(468\) −18.7000 −0.864406
\(469\) −29.0923 −1.34336
\(470\) 3.28832 0.151679
\(471\) −8.22862 −0.379155
\(472\) −19.5171 −0.898348
\(473\) −9.36364 −0.430541
\(474\) −5.91111 −0.271506
\(475\) 29.1606 1.33798
\(476\) 13.4040 0.614373
\(477\) −12.1265 −0.555233
\(478\) 51.2993 2.34638
\(479\) 1.69085 0.0772568 0.0386284 0.999254i \(-0.487701\pi\)
0.0386284 + 0.999254i \(0.487701\pi\)
\(480\) 2.69996 0.123236
\(481\) 4.65454 0.212229
\(482\) −11.8866 −0.541418
\(483\) −6.38865 −0.290693
\(484\) 115.484 5.24928
\(485\) 3.63286 0.164960
\(486\) 28.8994 1.31090
\(487\) 5.03381 0.228104 0.114052 0.993475i \(-0.463617\pi\)
0.114052 + 0.993475i \(0.463617\pi\)
\(488\) −1.88229 −0.0852073
\(489\) −7.46290 −0.337484
\(490\) 0.982809 0.0443988
\(491\) 37.8067 1.70619 0.853095 0.521755i \(-0.174722\pi\)
0.853095 + 0.521755i \(0.174722\pi\)
\(492\) −15.1223 −0.681767
\(493\) −0.502806 −0.0226452
\(494\) 19.0014 0.854911
\(495\) −3.78851 −0.170281
\(496\) 132.004 5.92714
\(497\) 35.7745 1.60470
\(498\) −1.36785 −0.0612950
\(499\) −10.7086 −0.479382 −0.239691 0.970849i \(-0.577046\pi\)
−0.239691 + 0.970849i \(0.577046\pi\)
\(500\) −13.6003 −0.608225
\(501\) −3.24145 −0.144817
\(502\) 84.5616 3.77417
\(503\) 10.1697 0.453445 0.226723 0.973959i \(-0.427199\pi\)
0.226723 + 0.973959i \(0.427199\pi\)
\(504\) 68.2584 3.04047
\(505\) 1.99795 0.0889077
\(506\) −101.011 −4.49049
\(507\) 4.86564 0.216091
\(508\) −49.8790 −2.21302
\(509\) 13.4689 0.597000 0.298500 0.954410i \(-0.403514\pi\)
0.298500 + 0.954410i \(0.403514\pi\)
\(510\) 0.277939 0.0123074
\(511\) −22.6419 −1.00162
\(512\) −109.656 −4.84616
\(513\) −14.3509 −0.633609
\(514\) 25.7218 1.13454
\(515\) 1.78026 0.0784474
\(516\) 3.98872 0.175594
\(517\) −27.6135 −1.21444
\(518\) −26.1656 −1.14965
\(519\) 1.81789 0.0797963
\(520\) −2.86054 −0.125443
\(521\) −13.9958 −0.613168 −0.306584 0.951844i \(-0.599186\pi\)
−0.306584 + 0.951844i \(0.599186\pi\)
\(522\) −3.94330 −0.172594
\(523\) −20.8191 −0.910356 −0.455178 0.890400i \(-0.650424\pi\)
−0.455178 + 0.890400i \(0.650424\pi\)
\(524\) 26.8427 1.17263
\(525\) 4.84996 0.211669
\(526\) −20.4935 −0.893561
\(527\) 7.71016 0.335860
\(528\) −39.9596 −1.73902
\(529\) 19.3868 0.842906
\(530\) −2.85681 −0.124092
\(531\) −5.36556 −0.232845
\(532\) −79.0838 −3.42872
\(533\) 7.36898 0.319186
\(534\) 13.3826 0.579122
\(535\) −0.229621 −0.00992738
\(536\) 127.230 5.49549
\(537\) −3.88069 −0.167464
\(538\) 37.7965 1.62952
\(539\) −8.25310 −0.355486
\(540\) 3.32723 0.143181
\(541\) −34.5215 −1.48419 −0.742097 0.670293i \(-0.766169\pi\)
−0.742097 + 0.670293i \(0.766169\pi\)
\(542\) −18.6317 −0.800302
\(543\) −10.1247 −0.434494
\(544\) −26.9615 −1.15597
\(545\) −3.99781 −0.171247
\(546\) 3.16028 0.135248
\(547\) 11.9374 0.510404 0.255202 0.966888i \(-0.417858\pi\)
0.255202 + 0.966888i \(0.417858\pi\)
\(548\) −5.88519 −0.251403
\(549\) −0.517471 −0.0220851
\(550\) 76.6829 3.26977
\(551\) 2.96656 0.126380
\(552\) 27.9396 1.18919
\(553\) −11.9884 −0.509799
\(554\) 13.1535 0.558837
\(555\) −0.401693 −0.0170509
\(556\) 29.2289 1.23958
\(557\) 2.70884 0.114777 0.0573886 0.998352i \(-0.481723\pi\)
0.0573886 + 0.998352i \(0.481723\pi\)
\(558\) 60.4677 2.55980
\(559\) −1.94367 −0.0822086
\(560\) 9.65083 0.407822
\(561\) −2.33399 −0.0985409
\(562\) −87.8454 −3.70553
\(563\) 17.5082 0.737884 0.368942 0.929452i \(-0.379720\pi\)
0.368942 + 0.929452i \(0.379720\pi\)
\(564\) 11.7628 0.495304
\(565\) −2.16974 −0.0912815
\(566\) 92.9000 3.90488
\(567\) 17.5362 0.736450
\(568\) −156.453 −6.56463
\(569\) 39.8886 1.67222 0.836108 0.548564i \(-0.184825\pi\)
0.836108 + 0.548564i \(0.184825\pi\)
\(570\) −1.63984 −0.0686855
\(571\) 29.9927 1.25516 0.627579 0.778553i \(-0.284046\pi\)
0.627579 + 0.778553i \(0.284046\pi\)
\(572\) 36.9943 1.54681
\(573\) −3.84072 −0.160448
\(574\) −41.4249 −1.72904
\(575\) −32.1781 −1.34192
\(576\) −114.693 −4.77888
\(577\) −16.4032 −0.682876 −0.341438 0.939904i \(-0.610914\pi\)
−0.341438 + 0.939904i \(0.610914\pi\)
\(578\) −2.77548 −0.115445
\(579\) −3.56236 −0.148047
\(580\) −0.687789 −0.0285589
\(581\) −2.77416 −0.115092
\(582\) 17.5524 0.727571
\(583\) 23.9899 0.993561
\(584\) 99.0205 4.09750
\(585\) −0.786407 −0.0325139
\(586\) 22.5477 0.931439
\(587\) 30.8716 1.27421 0.637104 0.770778i \(-0.280132\pi\)
0.637104 + 0.770778i \(0.280132\pi\)
\(588\) 3.51566 0.144983
\(589\) −45.4900 −1.87438
\(590\) −1.26404 −0.0520397
\(591\) −0.158715 −0.00652868
\(592\) 68.6759 2.82256
\(593\) −3.85567 −0.158334 −0.0791668 0.996861i \(-0.525226\pi\)
−0.0791668 + 0.996861i \(0.525226\pi\)
\(594\) −37.7383 −1.54842
\(595\) 0.563692 0.0231091
\(596\) 36.2419 1.48452
\(597\) 0.578287 0.0236677
\(598\) −20.9676 −0.857427
\(599\) −37.0008 −1.51181 −0.755906 0.654681i \(-0.772803\pi\)
−0.755906 + 0.654681i \(0.772803\pi\)
\(600\) −21.2104 −0.865911
\(601\) 40.9313 1.66962 0.834810 0.550538i \(-0.185577\pi\)
0.834810 + 0.550538i \(0.185577\pi\)
\(602\) 10.9264 0.445327
\(603\) 34.9774 1.42439
\(604\) −84.7871 −3.44994
\(605\) 4.85656 0.197447
\(606\) 9.65326 0.392137
\(607\) −42.9922 −1.74500 −0.872500 0.488614i \(-0.837503\pi\)
−0.872500 + 0.488614i \(0.837503\pi\)
\(608\) 159.073 6.45127
\(609\) 0.493394 0.0199933
\(610\) −0.121908 −0.00493591
\(611\) −5.73192 −0.231889
\(612\) −16.1156 −0.651434
\(613\) −37.9419 −1.53246 −0.766229 0.642567i \(-0.777869\pi\)
−0.766229 + 0.642567i \(0.777869\pi\)
\(614\) 80.6049 3.25295
\(615\) −0.635954 −0.0256441
\(616\) −135.036 −5.44077
\(617\) −7.15323 −0.287978 −0.143989 0.989579i \(-0.545993\pi\)
−0.143989 + 0.989579i \(0.545993\pi\)
\(618\) 8.60144 0.346000
\(619\) 30.1405 1.21145 0.605724 0.795675i \(-0.292883\pi\)
0.605724 + 0.795675i \(0.292883\pi\)
\(620\) 10.5467 0.423567
\(621\) 15.8359 0.635474
\(622\) 55.2431 2.21504
\(623\) 27.1414 1.08740
\(624\) −8.29467 −0.332053
\(625\) 24.1404 0.965617
\(626\) 32.1900 1.28657
\(627\) 13.7705 0.549942
\(628\) 112.401 4.48528
\(629\) 4.01127 0.159940
\(630\) 4.42081 0.176129
\(631\) 14.3719 0.572138 0.286069 0.958209i \(-0.407651\pi\)
0.286069 + 0.958209i \(0.407651\pi\)
\(632\) 52.4291 2.08552
\(633\) −5.87432 −0.233483
\(634\) 70.3520 2.79403
\(635\) −2.09761 −0.0832410
\(636\) −10.2192 −0.405219
\(637\) −1.71315 −0.0678775
\(638\) 7.80108 0.308848
\(639\) −43.0114 −1.70150
\(640\) −14.0867 −0.556826
\(641\) 15.0912 0.596068 0.298034 0.954555i \(-0.403669\pi\)
0.298034 + 0.954555i \(0.403669\pi\)
\(642\) −1.10943 −0.0437857
\(643\) 29.7690 1.17398 0.586988 0.809596i \(-0.300314\pi\)
0.586988 + 0.809596i \(0.300314\pi\)
\(644\) 87.2672 3.43881
\(645\) 0.167742 0.00660482
\(646\) 16.3753 0.644278
\(647\) 14.8389 0.583375 0.291688 0.956514i \(-0.405783\pi\)
0.291688 + 0.956514i \(0.405783\pi\)
\(648\) −76.6913 −3.01272
\(649\) 10.6147 0.416665
\(650\) 15.9176 0.624338
\(651\) −7.56584 −0.296529
\(652\) 101.941 3.99232
\(653\) −14.1951 −0.555495 −0.277748 0.960654i \(-0.589588\pi\)
−0.277748 + 0.960654i \(0.589588\pi\)
\(654\) −19.3157 −0.755304
\(655\) 1.12884 0.0441075
\(656\) 108.727 4.24506
\(657\) 27.2223 1.06204
\(658\) 32.2222 1.25615
\(659\) 35.8400 1.39613 0.698064 0.716035i \(-0.254045\pi\)
0.698064 + 0.716035i \(0.254045\pi\)
\(660\) −3.19266 −0.124274
\(661\) 42.4626 1.65160 0.825802 0.563960i \(-0.190723\pi\)
0.825802 + 0.563960i \(0.190723\pi\)
\(662\) 42.4475 1.64977
\(663\) −0.484481 −0.0188157
\(664\) 12.1323 0.470824
\(665\) −3.32579 −0.128969
\(666\) 31.4588 1.21900
\(667\) −3.27353 −0.126752
\(668\) 44.2773 1.71314
\(669\) −1.75620 −0.0678986
\(670\) 8.24013 0.318344
\(671\) 1.02372 0.0395202
\(672\) 26.4568 1.02060
\(673\) 19.6567 0.757711 0.378855 0.925456i \(-0.376318\pi\)
0.378855 + 0.925456i \(0.376318\pi\)
\(674\) −88.4378 −3.40650
\(675\) −12.0219 −0.462722
\(676\) −66.4633 −2.55628
\(677\) −11.5452 −0.443719 −0.221859 0.975079i \(-0.571213\pi\)
−0.221859 + 0.975079i \(0.571213\pi\)
\(678\) −10.4832 −0.402607
\(679\) 35.5983 1.36614
\(680\) −2.46521 −0.0945364
\(681\) −0.831854 −0.0318767
\(682\) −119.624 −4.58063
\(683\) 30.8821 1.18167 0.590836 0.806791i \(-0.298798\pi\)
0.590836 + 0.806791i \(0.298798\pi\)
\(684\) 95.0820 3.63555
\(685\) −0.247496 −0.00945632
\(686\) 55.2917 2.11105
\(687\) 10.9183 0.416560
\(688\) −28.6781 −1.09334
\(689\) 4.97975 0.189713
\(690\) 1.80953 0.0688876
\(691\) −26.1020 −0.992967 −0.496483 0.868046i \(-0.665376\pi\)
−0.496483 + 0.868046i \(0.665376\pi\)
\(692\) −24.8318 −0.943965
\(693\) −37.1236 −1.41021
\(694\) 36.0387 1.36801
\(695\) 1.22919 0.0466258
\(696\) −2.15777 −0.0817901
\(697\) 6.35057 0.240545
\(698\) −22.2773 −0.843207
\(699\) −5.69308 −0.215332
\(700\) −66.2491 −2.50398
\(701\) −10.9713 −0.414379 −0.207189 0.978301i \(-0.566432\pi\)
−0.207189 + 0.978301i \(0.566432\pi\)
\(702\) −7.83358 −0.295659
\(703\) −23.6665 −0.892600
\(704\) 226.898 8.55156
\(705\) 0.494673 0.0186305
\(706\) 2.77548 0.104456
\(707\) 19.5779 0.736303
\(708\) −4.52167 −0.169935
\(709\) 49.2734 1.85050 0.925251 0.379356i \(-0.123854\pi\)
0.925251 + 0.379356i \(0.123854\pi\)
\(710\) −10.1328 −0.380277
\(711\) 14.4136 0.540551
\(712\) −118.698 −4.44840
\(713\) 50.1972 1.87990
\(714\) 2.72352 0.101925
\(715\) 1.55576 0.0581820
\(716\) 53.0091 1.98104
\(717\) 7.71713 0.288202
\(718\) −9.59391 −0.358042
\(719\) 44.0695 1.64351 0.821757 0.569838i \(-0.192994\pi\)
0.821757 + 0.569838i \(0.192994\pi\)
\(720\) −11.6031 −0.432423
\(721\) 17.4447 0.649674
\(722\) −43.8804 −1.63306
\(723\) −1.78814 −0.0665015
\(724\) 138.301 5.13992
\(725\) 2.48511 0.0922945
\(726\) 23.4648 0.870862
\(727\) 6.11096 0.226643 0.113321 0.993558i \(-0.463851\pi\)
0.113321 + 0.993558i \(0.463851\pi\)
\(728\) −28.0304 −1.03888
\(729\) −18.0369 −0.668034
\(730\) 6.41313 0.237361
\(731\) −1.67505 −0.0619540
\(732\) −0.436084 −0.0161181
\(733\) −18.1496 −0.670372 −0.335186 0.942152i \(-0.608799\pi\)
−0.335186 + 0.942152i \(0.608799\pi\)
\(734\) 90.8207 3.35225
\(735\) 0.147847 0.00545343
\(736\) −175.534 −6.47025
\(737\) −69.1962 −2.54888
\(738\) 49.8049 1.83335
\(739\) 39.7553 1.46242 0.731211 0.682152i \(-0.238956\pi\)
0.731211 + 0.682152i \(0.238956\pi\)
\(740\) 5.48702 0.201707
\(741\) 2.85844 0.105007
\(742\) −27.9938 −1.02768
\(743\) −12.1880 −0.447136 −0.223568 0.974688i \(-0.571770\pi\)
−0.223568 + 0.974688i \(0.571770\pi\)
\(744\) 33.0878 1.21306
\(745\) 1.52411 0.0558392
\(746\) −5.52357 −0.202232
\(747\) 3.33536 0.122034
\(748\) 31.8816 1.16571
\(749\) −2.25005 −0.0822151
\(750\) −2.76340 −0.100905
\(751\) 21.4953 0.784374 0.392187 0.919886i \(-0.371719\pi\)
0.392187 + 0.919886i \(0.371719\pi\)
\(752\) −84.5723 −3.08404
\(753\) 12.7209 0.463575
\(754\) 1.61932 0.0589722
\(755\) −3.56563 −0.129767
\(756\) 32.6034 1.18578
\(757\) 10.3877 0.377546 0.188773 0.982021i \(-0.439549\pi\)
0.188773 + 0.982021i \(0.439549\pi\)
\(758\) −70.8010 −2.57161
\(759\) −15.1955 −0.551560
\(760\) 14.5447 0.527593
\(761\) 16.9604 0.614814 0.307407 0.951578i \(-0.400539\pi\)
0.307407 + 0.951578i \(0.400539\pi\)
\(762\) −10.1347 −0.367143
\(763\) −39.1744 −1.41821
\(764\) 52.4632 1.89805
\(765\) −0.677724 −0.0245032
\(766\) −54.2554 −1.96033
\(767\) 2.20337 0.0795591
\(768\) −34.1666 −1.23288
\(769\) 22.1586 0.799061 0.399530 0.916720i \(-0.369173\pi\)
0.399530 + 0.916720i \(0.369173\pi\)
\(770\) −8.74573 −0.315174
\(771\) 3.86942 0.139354
\(772\) 48.6608 1.75134
\(773\) −27.6299 −0.993778 −0.496889 0.867814i \(-0.665524\pi\)
−0.496889 + 0.867814i \(0.665524\pi\)
\(774\) −13.1367 −0.472191
\(775\) −38.1073 −1.36885
\(776\) −155.683 −5.58868
\(777\) −3.93618 −0.141210
\(778\) −101.630 −3.64362
\(779\) −37.4684 −1.34245
\(780\) −0.662722 −0.0237292
\(781\) 85.0899 3.04476
\(782\) −18.0698 −0.646174
\(783\) −1.22301 −0.0437067
\(784\) −25.2769 −0.902746
\(785\) 4.72689 0.168710
\(786\) 5.45409 0.194541
\(787\) 0.761315 0.0271380 0.0135690 0.999908i \(-0.495681\pi\)
0.0135690 + 0.999908i \(0.495681\pi\)
\(788\) 2.16801 0.0772321
\(789\) −3.08291 −0.109755
\(790\) 3.39561 0.120810
\(791\) −21.2612 −0.755961
\(792\) 162.353 5.76897
\(793\) 0.212500 0.00754609
\(794\) 60.3281 2.14096
\(795\) −0.429759 −0.0152420
\(796\) −7.89924 −0.279981
\(797\) −25.4190 −0.900387 −0.450194 0.892931i \(-0.648645\pi\)
−0.450194 + 0.892931i \(0.648645\pi\)
\(798\) −16.0688 −0.568829
\(799\) −4.93976 −0.174756
\(800\) 133.257 4.71134
\(801\) −32.6320 −1.15299
\(802\) −32.6044 −1.15130
\(803\) −53.8541 −1.90047
\(804\) 29.4762 1.03955
\(805\) 3.66993 0.129348
\(806\) −24.8311 −0.874638
\(807\) 5.68586 0.200152
\(808\) −85.6204 −3.01212
\(809\) −3.56651 −0.125392 −0.0626958 0.998033i \(-0.519970\pi\)
−0.0626958 + 0.998033i \(0.519970\pi\)
\(810\) −4.96697 −0.174522
\(811\) 15.2051 0.533923 0.266962 0.963707i \(-0.413980\pi\)
0.266962 + 0.963707i \(0.413980\pi\)
\(812\) −6.73963 −0.236515
\(813\) −2.80284 −0.0982998
\(814\) −62.2352 −2.18134
\(815\) 4.28703 0.150168
\(816\) −7.14833 −0.250241
\(817\) 9.88281 0.345756
\(818\) 79.3792 2.77543
\(819\) −7.70599 −0.269269
\(820\) 8.68695 0.303362
\(821\) 33.2592 1.16075 0.580376 0.814348i \(-0.302905\pi\)
0.580376 + 0.814348i \(0.302905\pi\)
\(822\) −1.19579 −0.0417081
\(823\) 4.12682 0.143852 0.0719259 0.997410i \(-0.477085\pi\)
0.0719259 + 0.997410i \(0.477085\pi\)
\(824\) −76.2912 −2.65773
\(825\) 11.5357 0.401620
\(826\) −12.3863 −0.430975
\(827\) −29.5582 −1.02784 −0.513919 0.857839i \(-0.671807\pi\)
−0.513919 + 0.857839i \(0.671807\pi\)
\(828\) −104.921 −3.64625
\(829\) −9.75878 −0.338937 −0.169468 0.985536i \(-0.554205\pi\)
−0.169468 + 0.985536i \(0.554205\pi\)
\(830\) 0.785757 0.0272740
\(831\) 1.97872 0.0686411
\(832\) 47.0988 1.63286
\(833\) −1.47639 −0.0511539
\(834\) 5.93892 0.205648
\(835\) 1.86204 0.0644384
\(836\) −188.102 −6.50563
\(837\) 18.7539 0.648230
\(838\) −30.3981 −1.05009
\(839\) 49.5613 1.71105 0.855523 0.517765i \(-0.173236\pi\)
0.855523 + 0.517765i \(0.173236\pi\)
\(840\) 2.41906 0.0834655
\(841\) −28.7472 −0.991282
\(842\) −54.4121 −1.87517
\(843\) −13.2149 −0.455145
\(844\) 80.2416 2.76203
\(845\) −2.79505 −0.0961525
\(846\) −38.7405 −1.33193
\(847\) 47.5894 1.63519
\(848\) 73.4742 2.52312
\(849\) 13.9753 0.479630
\(850\) 13.7177 0.470514
\(851\) 26.1155 0.895226
\(852\) −36.2466 −1.24179
\(853\) −33.2986 −1.14012 −0.570061 0.821602i \(-0.693081\pi\)
−0.570061 + 0.821602i \(0.693081\pi\)
\(854\) −1.19457 −0.0408775
\(855\) 3.99857 0.136748
\(856\) 9.84019 0.336331
\(857\) 9.25640 0.316192 0.158096 0.987424i \(-0.449464\pi\)
0.158096 + 0.987424i \(0.449464\pi\)
\(858\) 7.51676 0.256618
\(859\) 16.2887 0.555764 0.277882 0.960615i \(-0.410368\pi\)
0.277882 + 0.960615i \(0.410368\pi\)
\(860\) −2.29130 −0.0781328
\(861\) −6.23170 −0.212376
\(862\) 35.3188 1.20296
\(863\) −28.7258 −0.977839 −0.488919 0.872329i \(-0.662609\pi\)
−0.488919 + 0.872329i \(0.662609\pi\)
\(864\) −65.5802 −2.23108
\(865\) −1.04428 −0.0355065
\(866\) −82.8942 −2.81686
\(867\) −0.417524 −0.0141799
\(868\) 103.347 3.50784
\(869\) −28.5145 −0.967289
\(870\) −0.139750 −0.00473796
\(871\) −14.3635 −0.486689
\(872\) 171.322 5.80171
\(873\) −42.7996 −1.44855
\(874\) 106.612 3.60620
\(875\) −5.60450 −0.189467
\(876\) 22.9408 0.775096
\(877\) −40.0300 −1.35172 −0.675858 0.737032i \(-0.736227\pi\)
−0.675858 + 0.737032i \(0.736227\pi\)
\(878\) −93.6593 −3.16085
\(879\) 3.39193 0.114407
\(880\) 22.9546 0.773799
\(881\) −57.1257 −1.92461 −0.962307 0.271966i \(-0.912326\pi\)
−0.962307 + 0.271966i \(0.912326\pi\)
\(882\) −11.5787 −0.389876
\(883\) −16.5703 −0.557635 −0.278818 0.960344i \(-0.589943\pi\)
−0.278818 + 0.960344i \(0.589943\pi\)
\(884\) 6.61788 0.222583
\(885\) −0.190154 −0.00639196
\(886\) 41.3779 1.39012
\(887\) 8.19913 0.275300 0.137650 0.990481i \(-0.456045\pi\)
0.137650 + 0.990481i \(0.456045\pi\)
\(888\) 17.2142 0.577670
\(889\) −20.5544 −0.689373
\(890\) −7.68758 −0.257688
\(891\) 41.7099 1.39734
\(892\) 23.9892 0.803218
\(893\) 29.1446 0.975287
\(894\) 7.36387 0.246285
\(895\) 2.22924 0.0745154
\(896\) −138.035 −4.61143
\(897\) −3.15422 −0.105316
\(898\) −36.3450 −1.21285
\(899\) −3.87672 −0.129296
\(900\) 79.6508 2.65503
\(901\) 4.29153 0.142972
\(902\) −98.5296 −3.28068
\(903\) 1.64370 0.0546988
\(904\) 92.9821 3.09254
\(905\) 5.81610 0.193334
\(906\) −17.2276 −0.572349
\(907\) 19.0545 0.632694 0.316347 0.948643i \(-0.397544\pi\)
0.316347 + 0.948643i \(0.397544\pi\)
\(908\) 11.3629 0.377091
\(909\) −23.5384 −0.780719
\(910\) −1.81541 −0.0601802
\(911\) −12.4631 −0.412920 −0.206460 0.978455i \(-0.566194\pi\)
−0.206460 + 0.978455i \(0.566194\pi\)
\(912\) 42.1752 1.39656
\(913\) −6.59837 −0.218374
\(914\) −90.5904 −2.99646
\(915\) −0.0183390 −0.000606270 0
\(916\) −149.141 −4.92777
\(917\) 11.0615 0.365283
\(918\) −6.75096 −0.222815
\(919\) 22.1311 0.730038 0.365019 0.931000i \(-0.381063\pi\)
0.365019 + 0.931000i \(0.381063\pi\)
\(920\) −16.0498 −0.529146
\(921\) 12.1257 0.399554
\(922\) −47.5547 −1.56613
\(923\) 17.6627 0.581374
\(924\) −31.2848 −1.02919
\(925\) −19.8256 −0.651862
\(926\) 16.2730 0.534762
\(927\) −20.9736 −0.688864
\(928\) 13.5564 0.445012
\(929\) 49.6112 1.62769 0.813845 0.581082i \(-0.197371\pi\)
0.813845 + 0.581082i \(0.197371\pi\)
\(930\) 2.14296 0.0702704
\(931\) 8.71070 0.285482
\(932\) 77.7659 2.54731
\(933\) 8.31040 0.272070
\(934\) 55.2372 1.80742
\(935\) 1.34075 0.0438471
\(936\) 33.7007 1.10154
\(937\) 17.9491 0.586371 0.293185 0.956056i \(-0.405285\pi\)
0.293185 + 0.956056i \(0.405285\pi\)
\(938\) 80.7449 2.63641
\(939\) 4.84244 0.158027
\(940\) −6.75710 −0.220392
\(941\) 18.2934 0.596349 0.298174 0.954511i \(-0.403622\pi\)
0.298174 + 0.954511i \(0.403622\pi\)
\(942\) 22.8383 0.744113
\(943\) 41.3455 1.34640
\(944\) 32.5099 1.05811
\(945\) 1.37110 0.0446020
\(946\) 25.9886 0.844961
\(947\) 51.1789 1.66309 0.831546 0.555456i \(-0.187456\pi\)
0.831546 + 0.555456i \(0.187456\pi\)
\(948\) 12.1466 0.394504
\(949\) −11.1788 −0.362881
\(950\) −80.9346 −2.62587
\(951\) 10.5833 0.343187
\(952\) −24.1565 −0.782917
\(953\) 14.5224 0.470426 0.235213 0.971944i \(-0.424421\pi\)
0.235213 + 0.971944i \(0.424421\pi\)
\(954\) 33.6567 1.08968
\(955\) 2.20629 0.0713937
\(956\) −105.414 −3.40933
\(957\) 1.17354 0.0379352
\(958\) −4.69290 −0.151621
\(959\) −2.42520 −0.0783139
\(960\) −4.06469 −0.131187
\(961\) 28.4466 0.917633
\(962\) −12.9186 −0.416511
\(963\) 2.70522 0.0871745
\(964\) 24.4255 0.786691
\(965\) 2.04638 0.0658753
\(966\) 17.7315 0.570503
\(967\) 23.1948 0.745893 0.372946 0.927853i \(-0.378348\pi\)
0.372946 + 0.927853i \(0.378348\pi\)
\(968\) −208.124 −6.68934
\(969\) 2.46340 0.0791357
\(970\) −10.0829 −0.323743
\(971\) 16.8217 0.539833 0.269916 0.962884i \(-0.413004\pi\)
0.269916 + 0.962884i \(0.413004\pi\)
\(972\) −59.3848 −1.90477
\(973\) 12.0448 0.386139
\(974\) −13.9712 −0.447667
\(975\) 2.39453 0.0766865
\(976\) 3.13535 0.100360
\(977\) −54.9587 −1.75828 −0.879142 0.476560i \(-0.841884\pi\)
−0.879142 + 0.476560i \(0.841884\pi\)
\(978\) 20.7131 0.662332
\(979\) 64.5562 2.06322
\(980\) −2.01955 −0.0645123
\(981\) 47.0992 1.50376
\(982\) −104.931 −3.34850
\(983\) 18.3612 0.585632 0.292816 0.956169i \(-0.405408\pi\)
0.292816 + 0.956169i \(0.405408\pi\)
\(984\) 27.2532 0.868800
\(985\) 0.0911733 0.00290502
\(986\) 1.39553 0.0444426
\(987\) 4.84729 0.154291
\(988\) −39.0455 −1.24220
\(989\) −10.9055 −0.346773
\(990\) 10.5149 0.334187
\(991\) −23.6819 −0.752282 −0.376141 0.926563i \(-0.622749\pi\)
−0.376141 + 0.926563i \(0.622749\pi\)
\(992\) −207.878 −6.60013
\(993\) 6.38553 0.202639
\(994\) −99.2912 −3.14932
\(995\) −0.332194 −0.0105313
\(996\) 2.81077 0.0890628
\(997\) −18.6026 −0.589149 −0.294575 0.955628i \(-0.595178\pi\)
−0.294575 + 0.955628i \(0.595178\pi\)
\(998\) 29.7214 0.940816
\(999\) 9.75686 0.308693
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 6001.2.a.d.1.1 121
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6001.2.a.d.1.1 121 1.1 even 1 trivial